InvestorQ : How does a decrease in the stock price impact the value of the put option on a particular stock and why is that so?
Priyanka Jain made post

How does a decrease in the stock price impact the value of the put option on a particular stock and why is that so?

Answer
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Mary Joseph answered.
1 year ago


Let us understand this better with an illustration of a real life example where the stock price actually moves down and let us see the impact on the value of the put option.

Input Data

Input Data

Stock Price now (P)

120

Stock Price now (P)

115

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

Number of periods to Exercise in years (t)

0.083333333

Number of periods to Exercise in years (t)

0.083333333

Compounded Risk-Free Interest Rate (rf)

5.00%

Compounded Risk-Free Interest Rate (rf)

5.00%

Standard Deviation (annualized s)

30.00%

Standard Deviation (annualized s)

30.00%

Output Data

Output Data

Present Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

124.4803

s*t^0.5

0.0866

s*t^0.5

0.0866

d1

-0.3800

d1

-0.8714

d2

-0.4666

d2

-0.9580

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.1918

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

21.0412

Value of Put

6.8345

Value of Put

10.4926

In the above instance we have assumed that all the factors remain constant but only the stock price goes down from Rs.120 to Rs.115. You will see that the value of the put option also goes up. That is because a put option is a right to sell the stock at the strike price, which is Rs.125 in this case. As the stock price keeps going down it becomes more and more in the money and hence the put becomes more valuable. What happens to the option value as the price goes down further. Will the put option value grow at a faster rate or a slower rate? Let us simulate another situation with an additional Rs.5 decrease in the stock price. What happens? Check our workings below:

Input Data

Input Data

Stock Price now (P)

120

Stock Price now (P)

110

Exercise Price of Option (EX)

125

Exercise Price of Option (EX)

125

Number of periods to Exercise in years (t)

0.083333333

Number of periods to Exercise in years (t)

0.083333333

Compounded Risk-Free Interest Rate (rf)

5.00%

Compounded Risk-Free Interest Rate (rf)

5.00%

Standard Deviation (annualized s)

30.00%

Standard Deviation (annualized s)

30.00%

Output Data

Output Data

Present Value of Exercise Price (PV(EX))

124.4803

Present Value of Exercise Price (PV(EX))

124.4803

s*t^0.5

0.0866

s*t^0.5

0.0866

d1

-0.3800

d1

-1.3847

d2

-0.4666

d2

-1.4713

Delta N(d1) Normal Cumulative Density Function

0.3520

Delta N(d1) Normal Cumulative Density Function

0.0831

Bank Loan N(d2)*PV(EX)

39.8844

Bank Loan N(d2)*PV(EX)

8.7892

Value of Put

6.8345

Value of Put

14.8293

When the stock price goes down by another Rs.5 to Rs.110, then the value of the put option goes up further to Rs.14.8293. But you will also notice that the percentage rise is lower in the second round than the first round. That is because the option value has two components viz. the time value and the intrinsic value. As the stock price goes below Rs.125 which is the strike price, it acquires higher intrinsic value also, apart from time value. Thus the impact of time value on the total option valuation keeps going down consistently. This trend will continue as you keep going further down.